Poincaré Maps - Dynamical Systems | Lecture 28

In this lecture we will talk about work from my favourite mathematician and one of my favourite topics in all of dynamical systems - Poincaré maps! Although many systems of interest in the real world are continuous in time, they are complex and hard to analyze. Poincaré's brilliant idea was to introduce a hyperplane into the phase space and simply track the intersection of trajectories with this hyperplane. The result is a discrete sequence of intersections, with the theoretical map/rule that iterates through the sequence being called a Poincaré map. Here we review the basics and provide some examples where the map can be computed explicitly. Check out some of my own research into learning Poincaré maps from data:    • Discovering Poincare Mappings | Video Abst...   Brush up on variation of parameters with my lecture on it:    • Variation of Parameters - Ordinary Differe...   This course is taught by Jason Bramburger for Concordia University. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.